7.10 摘要:单位圆圈和三角函数

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• 选择节摘要:单位圆圈和三角函数

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  摘要:单位圆圈和三角函数

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  Chapter Summary
  ::章次摘要

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  We've learned many tools in  this chapter to understand how to graph trigonometric functions .  
  ::我们在本章中学习了许多工具 来了解如何绘制三角函数

  

   

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  We've learned about:
  ::我们学到了:

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  The Unit Circle
  ::联合圆圈

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  • The unit circle provides a basis for understanding how the sine, cosine, and tangent ratios relate.  
    ::单位圆为了解正弦、正弦和正弦之比之间的关系提供了一个基础。
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  • The unit circle is a circle with its center at the origin and with a radius of 1, whose equation is  $\begin{array}{r}{x}^2+y^2=1.\end{array}$   
    ::单位圆是一个圆形,其中心位于原点,半径为1,其方程式为 x2+y2=1。

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  Graphing  Trigonometric Functions
  ::三角函数图

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  • Sinusoidal functions have the form  $\begin{array}{r}f(x)=a\sin (b\left(x-h)\right)+k,\end{array}$  where $\begin{array}{r}|a|\end{array}$   is the  amplitude ,  $\begin{array}{r}h\end{array}$   is the horizontal or  phase shift, and $\begin{array}{r}k\end{array}$  is the vertical shift.  The period is   $\begin{array}{r}\frac{2\pi }{\left|b\right|}\end{array}$  and the frequency is $\begin{array}{r}\frac{\left|b\right|}{2\pi }\end{array}$ .
    ::Sinusoidal 函数为 f( x) =asin {( b( x- h))+k, 其中 {a} {a} 是振幅, h 是水平或相位变化, k 是垂直变化。 周期为 2 {b} , 频率为 {b} 2 。
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  • Since  cosecant is the reciprocal of the sine function, and secant is the reciprocal of the cosine function, t he secant and cosecant graphs can be sketched by sketching a faint sine or cosine graph and using that graph to establish asymptotes.
    ::由于共生体是正弦函数的对等函数,分离是正弦函数的对等函数,分离和共生体图形可以通过绘制一个微弱正弦或正弦图形,并利用该图来建立静脉图来绘制草图。
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  • To graph the tangent and cotangent functions, determine the asymptotes and zeros of the functions  using the knowledge of the ratio of sine and cosine functions.
    ::要绘制正切和余切函数图,请使用对正弦函数和正弦函数之比的了解来确定函数的零点和零点。

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  Inverse Trigonometric Functions
  ::反逆三角函数

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  • There are two conventions used to identify inverse trigonometric functions: using the prefix of arc, or the superscript of -1. 
    ::有两项公约用来确定反三角函数:使用弧的前缀或-1的上标。
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  • Even though none of the trigonometric functions pass the horizontal line test over the entire set of  real numbers , their domains can be restricted for the purpose of studying and applying inverses.
    ::即使三角函数没有一个能通过横线测试,超过整个一套实际数字,但为了研究和应用反向,它们的域可以加以限制。

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  Review
  ::回顾

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  Try the following cumulative review problems to practice the concepts in this chapter:
  ::尝试下列累积审查问题来实践本章中的概念: